25) \( 2 x y-8 x^{2}+7 y^{3}-28 y^{2} x \)

The expression \( 2xy - 8x^{2} + 7y^{3} - 28y^{2}x \) can be factored by grouping. Start by rearranging it as \( -8x^{2} + 2xy - 28y^{2}x + 7y^{3} \). Group it as \( (-8x^{2} + 2xy) + (-28y^{2}x + 7y^{3}) \). Factoring each group gives \( -2x(4x - y) + 7y^{2}(y - 4x) \). Notice that everything can be organized to produce the factor \((4x - y)\). The complete factorization is \((4x - y)(-2x + 7y^{2})\). Next, you can think of ways this expression might pop up in real-world situations! For instance, if you're working on optimizing a certain area in a garden with crops \(x\) and \(y\), this polynomial could represent a relationship in planting constraints or yield based on different crop interactions. Understanding the factored form can aid in visualizing how changes in one crop's area might affect your total yield or cost!